Problem: Rafaela is a physical education teacher and has $25$ girls and $35$ boys in her class. She wants to divide the class into teams of the same size, where each team has the same number of girls and the same number of boys. If Rafaela creates the greatest number of teams possible, how many boys will be on each team?
Explanation: In order to know how many teams Rafaela can create, we need a number that is a factor of ${25}$ and ${35}$, so that the ${25}$ girls and the ${35}$ boys can be divided up evenly. To find the greatest number of teams, we want to find the greatest common factor of ${25}$ and ${35}$. To do so, let's find factors of ${25}$ and ${35}$. ${25}$ : $1, 5, 25$ ${35}$ : $1,5, 7, 35$ The greatest common factor of ${25}$ and ${35}$ is $5$. In math notation this looks like: $ \text{gcf}({25}, {35}) = 5$. The greatest number of teams that Rafaela can make is $5$. To find the number of boys on each team, we need to divide the total number of boys by the number of teams: $ {35} \div 5 = 7.$ There will be $7$ boys on each team.